Electrical machines with reduced cogging

ABSTRACT

An electrical machine has at least two separate groups of at least two circumferentially adjacent magnet poles. One of the circumferentially outer magnet poles in one of the groups of magnet poles is defined as being in its reference position. The reference position of each other magnet pole is defined as the position each other magnet pole would occupy if all the magnet poles were equally circumferentially spaced around the first or second body and the one circumferentially outer pole was in its reference position. At least one of the circumferentially outer magnet poles in each group is sited in its reference position. At least one magnet pole in each group is a displaced magnet pole and is sited in a position that is displaced from its reference position by an amount that is not equal to an integral multiple of the reference angular pitch of the winding slots. The displacement of the magnet poles provides a pronounced reduction in cogging.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of U.S. patent applicationSer. No. 11/787,724, filed Apr. 17, 2007, now pending.

FIELD OF THE INVENTION

This invention relates to permanent-magnet based, alternating current,rotating electrical machines and the minimizing of cogging torqueexhibited by such machines. In particular, it relates to electricalmachines with reduced cogging due to the displacement of their magnetpoles.

BACKGROUND OF THE INVENTION

A common problem encountered in the operation of electrical machines iscogging. Cogging is the presence of non-linear magnetic torque duringthe operation of the machine due to the effect of the geometry of therotor and the stator at the air gap on the flux distribution and theforces between the rotor and the stator. Specifically, it is caused bythe rotor having preferred low potential energy positions relative tothe stator, where the attraction between the rotor and stator is at amaximum, and corresponding high potential energy positions disposedbetween each of the low energy positions. It is the difference inpotential energy between these positions that determines the magnitudeof the cogging torque.

Cogging during the operation of electrical machines can result indecreased efficiency and reliability, as well as causing unwantedvibration and noise and, in extreme cases, complete failure. Cogging iswell known in machines in which the stator, the rotor, or both the rotorand the stator exhibit some form of saliency. The effect is also wellknown in induction machines in which the magnet poles and winding slotsinteract to cause serious cogging for particular numbers of windingslots. Cogging is particularly pronounced in machines which have anumber of winding slots that is an integral multiple of the number ofmagnet poles and where both the winding slots and magnet poles areuniformly spaced around the circumference of the bodies in which theyare formed. This is because, due to the symmetry of such machines, whenone magnet pole is in its lowest potential energy position relative tothe winding slots, all the other magnet poles will also be in theirlowest potential energy position and the rotor will therefore be in thelowest possible potential energy position relative to the stator.Furthermore, this means if there are n winding slots the rotor will haven low potential energy positions relative to the stator and the coggingfrequency during operation of the machine will be a product of therotation frequency of the rotor and n.

Typical permanent-magnet based electrical machines are formed such thatthe rotor is rotatably mounted within the stator, the magnet poles areuniformly spaced around the circumference of the outer surface of therotor and the winding slots are uniformly spaced around thecircumference of the inner surface of the stator. However, otherconstructions are also possible. For example, it is possible that therotor is rotatably mounted outside the stator. It is also possible forthe magnet poles to be fixed to the stator and the winding slots to beformed in the rotor. With regards to cogging, the design considerationsfor permanent-magnet based electrical machines according to any of theseconstructions are substantially the same.

The factors that must be considered when deciding upon the number ofwinding slots in an electrical machine are generally well known. Forexample, it is known that when an electrical machine has a number ofwinding slots which is an integral multiple of the number of its magnetpoles the magneto-motive force (m.m.f.) created by the machine's statorwinding during operation will contain a minimized number of harmonicsbut the machine may also experience pronounced cogging during operation.

Numerous methods of minimizing cogging have been proposed andimplemented with varying degrees of success. For some types of machineit is possible to minimize cogging by having a number of winding slotsthat is not an integral multiple of the number of magnet poles. Suchwindings are generally referred to as comprising ‘fractional slots perpole per phase’ and are well known to those who are skilled in the art.However, in some cases this may not be preferred, or even possible. Forexample, in large-scale electrical machines the options for havingdiffering numbers of winding slots that are not multiples of the numberof magnet poles are very limited as the non-synchronous flux patternsthat result from such changes in the number of winding slots inevitablylead to additional losses in the magnet poles. These losses may beextremely high and even render the method unusable.

An alternative method of reducing cogging is to incorporate magneticwedges in the winding slots but this method is costly. It is alsopossible to use ‘semi-closed’ winding slots to reduce cogging but forthe types of winding that comprise formed coils and are common in largemachines this type of winding slot can lead to an unacceptably highwinding cost. Permanent-magnet machines that have magnet polesspecifically shaped to reduce cogging have also been proposed.Typically, it is proposed that the outer surfaces of the magnet polesare formed such that the air gap between the stator and the magnet polesis not uniform.

Another method of minimizing cogging torque in permanent-magnet basedelectrical machines is to have the magnets skewed from theirconventional arrangement. For example, Japanese Patent No. 2005-261188discloses a machine with reduced cogging in which the magnets are skewedsuch that they are not parallel with the axis of the machine.

A further method of minimizing cogging torque is disclosed in U.S. Pat.No. 4,713,569, which discloses an AC electric motor with apermanent-magnet rotor containing a plurality of magnet poles that areangularly displaced from their reference positions by an amountdependent upon the number of magnet poles and the number of stator poles(winding slots) in the machine. The reference positions of the magnetpoles are the positions where they would be situated were they equallyspaced circumferentially. Specifically, in electrical machines accordingto this U.S. patent, each magnet pole is displaced from its referenceposition by a different amount, the differing amounts all being integralmultiples of 360° divided by the product of the number of stator poles(winding slots) and the number of magnet poles, such that no magnet poleis displaced from its reference position by more than the pitch of thestator poles (winding slots). The specific example given in thespecification of this U.S. patent is of an AC electric motor with apermanent-magnet rotor with 8 magnet poles and a stator with 24 poles(winding slots) and wherein the magnet poles are displaced from theirreference positions by integral multiples of 1.875° (360°/(24×8)) suchthat no two poles are displaced from their reference positions by thesame amount and the (nominal) 8^(th) magnet pole is displaced from itsreference position by an amount equal to the stator pole (winding slot)pitch.

The rotor construction disclosed in U.S. Pat. No. 4,713,569 provides asubstantial reduction in cogging torque as compared to conventionalelectrical machines with uniformly spaced magnet poles. However, in mostcases this rotor construction will not be preferred to the conventionalconstruction due to its impact on other design considerations. Forexample, this construction results in complete asymmetry of thepositioning of the magnet poles around the rotor. If the electricalmachine is intended for high-speed use, then this asymmetry isundesirable as it means the magnet pole arrangement is not mechanicallybalanced. This complete asymmetry also results in a pronounced harmoniccontent of either the m.m.f. created by the stator winding if themachine is a motor or the electro-motive force (e.m.f.) waveform createdin the stator winding if the machine is a generator.

The rotor construction of U.S. Pat. No. 4,713,569 may also not bepreferred due to the separation of the first and last magnet poles asdefined in that patent. This is because the angular separation betweenthese two magnet poles is significantly less than in a conventionalelectrical machine with uniformly spaced magnet poles. Specifically, theseparation between these two poles is less than the uniform spacing byan amount equal to the winding slot pitch. Depending upon the angularwidth of the magnets that form these magnet poles, this could lead tothe two magnet poles being in contact with or impinging upon oneanother, which is generally undesirable, as discussed later.

Finally, the strict requirement for the positioning of the magnet polesalso leads to a lack of flexibility in the design of machines accordingto U.S. Pat. No. 4,713,569.

That is, the positions of the magnet poles cannot be altered in responseto any other design consideration.

SUMMARY OF THE INVENTION

In a first arrangement, the present invention provides an electricalmachine including a first body having a plurality of circumferentiallyspaced winding slots formed at its radially inner surface, and a secondbody, that is located within the first body, and having a plurality ofcircumferentially spaced magnet poles formed at its radially outersurface, one of the first body and the second body being a rotor androtatably mounted and the other of the first body and the second bodybeing a stator and being fixedly mounted, the winding slots having areference angular pitch that is equal to 360° divided by the number ofwinding slots in the electrical machine; the magnet poles comprising atleast a first group including at least two circumferentially adjacentmagnet poles and a second group including at least two circumferentiallyadjacent magnet poles; each magnet pole having a reference positionwherein the reference positions are equally spaced around thecircumference of the second body; at least one magnet pole in each ofthe first and second groups being a circumferentially outermost magnetpole and being located in its reference position; and at least onemagnet pole in each of the first and second groups being a displacedmagnet pole and being located in a position that is displaced from itsreference position by an amount that is not equal to an integralmultiple of the reference angular pitch of the winding slots.

In a second arrangement, the present invention provides an electricalmachine including a first body having a plurality of circumferentiallyspaced magnet poles formed at its radially inner surface, and a secondbody, that is located within the first body, and having a plurality ofcircumferentially spaced winding slots formed at its radially outersurface, one of the first body and the second body being a rotor androtatably mounted and the other of the first body and the second bodybeing a stator and being fixedly mounted, the winding slots having areference angular pitch that is equal to 360° divided by the number ofwinding slots in the electrical machine; the magnet poles comprising atleast a first group including at least two circumferentially adjacentmagnet poles and a second group including at least two circumferentiallyadjacent magnet poles; each magnet pole having a reference positionwherein the reference positions are equally spaced around thecircumference of the first body; at least one magnet pole in each of thefirst and second groups being a circumferentially outermost magnet poleand being located in its reference position; and at least one magnetpole in each of the first and second groups being a displaced magnetpole and being located in a position that is displaced from itsreference position by an amount that is not equal to an integralmultiple of the reference angular pitch of the winding slots.

The magnet poles can be formed on the stator and the winding slots canbe formed in the rotor. However, it is generally preferred that themagnet poles are formed on the rotor and the winding slots are formed inthe stator. For ease of comprehension, the following discussion of theissues relating to electrical machines according to this inventionrefers to electrical machines where the magnet poles are formed on therotor and the winding slots are formed in the stator. However, it is tobe understood that electrical machines according to this invention mayalso be constructed where the magnet poles are formed on the stator andthe winding slots are formed in the rotor and the following discussionapplies equally to either configuration, unless otherwise specified.

It is envisaged that it will generally be preferred that electricalmachines according to this invention will be constructed such that thefirst body is the stator and the second body is the rotor. That is, thatthe rotor is rotatably mounted within the stator. However, it is to beunderstood that electrical machines according to this invention whereinthe rotor is the first body and is rotatably mounted outside the secondbody, which is the stator, are equally possible and may even bepreferred for some applications. The following discussion appliesequally to either configuration, unless otherwise specified.

An electrical machine according to this invention will have at least twomagnet pole groups. Each group will include at least twocircumferentially adjacent magnet poles. This means that each group willinclude two circumferentially outermost magnet poles being those magnetpoles that are at the outermost edges of the group and which will becircumferentially adjacent to a magnet pole in another group. If thereare only two magnet poles in each group, then there will be no magnetpoles located between the circumferentially outermost magnet poles.However, if there are three or more magnet poles in each group, thenthere will be at least one magnet pole located between thecircumferentially outermost magnet poles. Such a magnet pole can bedescribed as an ‘inner’ magnet pole.

At least one of the circumferentially outermost magnet poles in eachgroup is located in its reference position. Any magnet poles that islocated in its reference position can be described as an ‘undisplaced’magnet pole. At least one of the magnet poles in each group (meaning anymagnet pole apart from said circumferentially outermost magnet pole thatis located at its reference position) is a ‘displaced’ magnet pole thatis located in a position that is displaced from its reference positionby an amount that is not equal to an integral multiple of the referenceangular pitch of the winding slots. Any remaining magnet poles in eachgroup can be either an undisplaced magnet pole and located at itsreference position or a displaced magnet pole and displaced from itsreference position.

The reference position of each magnet pole can be understood in thefollowing manner. The design of any electrical machine according to thisinvention can be considered to be formed by taking the design of therotor of a conventional electrical machine that has the magnet polesequally spaced around its circumference and circumferentially displacingsome of the magnet poles. The position each magnet pole would haveoccupied in that conventional electrical machine is its referenceposition. That is, the reference positions for an electrical machineaccording to the present invention are equally spaced around thecircumference of the body in which the magnet poles are formed. Themagnet poles that do not occupy their reference positions are thedisplaced magnet poles. In this manner, the displaced magnet poles, themagnet pole groups and the reference position of each magnet pole may bedefined simply. Since each magnet pole has a corresponding referenceposition, it will be appreciated that any given electrical machine willhave the same number of magnet poles and reference positions. Thus, ifthe electrical machine has one hundred and twelve magnet poles(optionally arranged in fourteen magnet pole groups, each groupincluding eight magnet poles), then the electrical machine will alsohave one hundred and twelve reference positions equally spaced aroundthe circumference of the body in which the magnet poles are formed. Atleast one of the circumferentially outermost magnet poles of each groupwill be located at its reference position, at least one of the magnetpoles of each group will be displaced from its reference position, andthe remaining magnet poles of each group can be either undisplacedmagnet poles or displaced magnet poles depending on the desireddisplacement pattern.

The pitch of any object is defined as the angular or linearcircumferential separation of the equivalent points on two adjacentcircumferentially spaced objects. Therefore, the winding slot pitch isdefined as the circumferential separation between the equivalent pointson two adjacent winding slots. If an electrical machine has radiallysymmetrical winding slots, then the linear winding slot pitch may bedefined as the circumferential separation between the slot centre-linesof two adjacent winding slots as measured around the surface of the bodyin which they are formed. The winding slot pitch may also be expressedas an angle which, if expressed in radians, is equal to the linearwinding slot pitch divided by the radius of the body in which the slotsare formed. The reference angular pitch of the winding slots, whenexpressed in degrees, is equal to 360° divided by the number of windingslots contained in the machine and, when expressed in radians, is equalto 2π divided by the number of winding slots.

The winding slots will preferably each be identical and be uniformlyspaced. That is, their actual pitch will be equal to their referencepitch. However, electrical machines that have winding slots that arenon-identical and/or that are not uniformly spaced are also possible.The presence of non-uniformly spaced winding slots would affect theoperation and behavior of electrical machines according to thisinvention in substantially the same manner as for conventionalelectrical machines, as would be apparent to a person skilled in theart. As the positioning of the winding slots affects the operation ofmachines according to this invention, this needs to be considered alongwith the other design considerations described in this specificationwhen defining the displacement pattern of the magnet poles in anelectrical machine according to this invention.

Electrical machines according to this invention will generally have anumber of winding slots that is an integral multiple of the number ofmagnet poles. However, for some machines according to this invention, itmay be possible to reduce cogging further by having a number of windingslots that is not an integral multiple of the number of magnet poles,i.e., a ‘fractional slots per pole per phase’ winding. However,generally such designs will not be preferred, or even possible as thenon-synchronous flux patterns that result from ‘fractional slots perpole per phase’ windings inevitably lead to additional losses in themagnet poles, as discussed earlier.

The reference angular pitch of the magnet poles is defined as 360°divided by the number of magnet poles in the machine.

The presence of displaced magnet poles in machines according to thisinvention leads to a reduction in cogging due to its effect on thepotential energy of the relative positions of the rotor relative to thestator. Specifically, displacing the magnet poles reduces the magnitudeof the potential energy difference between the rotor's highest andlowest potential energy positions relative to the stator. This isbecause when the magnet poles are not uniformly spaced around thecircumference of the rotor, when any one individual magnet pole is inits lowest possible potential energy position relative to the windingslots, any other magnet pole that is displaced from its referenceposition relative to that individual magnet pole by an amount that isnot an integral multiple of the winding slot pitch will be in a higherpotential energy position relative to the winding slots. This means thatthe overall potential energy of the rotor in that position will beraised compared to the equivalent position of a rotor which has magnetpoles uniformly spaced at integral multiples of the winding slot pitch.An equivalent argument applies to the high energy positions of therotor. That is, the presence of displaced magnet poles lowers the energyof the high potential energy positions of the rotor relative to thestator.

The raising of the energy of the low potential energy positions and thelowering of the energy of the high potential energy positions of therotor relative to the stator results in a reduction in the coggingtorque. The magnitude of the reduction in cogging torque depends on thespecific displacement pattern of the magnet poles that is used in anymachine but it can be very pronounced. The displacement of the magnetpoles also results in an increase in cogging frequency as thedisplacement of some of the magnet poles results in an increase in thenumber of low and high potential energy positions of the rotor relativeto the stator.

The effectiveness of the displacement of the magnet poles in reducingcogging is also influenced by a number of additional factors which mustalso be considered. Such factors include the width of each magnet polerelative to the winding slot pitch and the ratio of the winding slotopening to the winding slot pitch. These parameters influence thealignment of the m.m.f. pattern of the magnet poles with the permeancevariations caused by the winding slots which, in turn, affects themagnitude of the energy of the low and high potential energy positionsThere are many shapes of winding slots that are commonly used and whoseeffects will be well known to a person skilled in the art.

Although, theoretically, the minimum possible cogging torque is achievedif each magnet pole is displaced by less than the winding slot pitch andby a different amount, as in an electrical machine according to U.S.Pat. No. 4,713,569, for the reasons discussed earlier, this pattern isnot usually preferred. The displacement of the magnet poles as definedherein is generally preferable as it may enable the stator or rotor tobe constructed more easily and furthermore, displacement patternsaccording to the present application may be sufficiently simple toenable the behavior of the machine to be modelled and analyzed easily.If the displacement of the magnet poles around the rotor or the statoris too complex, computer analysis of the behavior of the machine duringoperation, though possible in principle, may become excessivelydifficult. If the behavior of a machine cannot be analyzed easily, it isdifficult to modify the design in response to other considerations, suchas voltage waveform harmonics.

If an electrical machine according to this invention is intended forhigh-speed use, it is preferable that the magnet pole arrangement doesnot result in the rotor being mechanically unbalanced. This can beensured by having the magnets that form the magnet poles displacedaround the rotor in a pattern that has at least two-fold rotationalsymmetry about its axis. One way of achieving this symmetry is to have arotor with the same number of magnet poles in each group and the samedisplacement pattern of magnet poles within each group, as disclosed inthe displacement patterns below.

Rotors with rotationally symmetrical displacement patterns of magnetpoles are also preferred as they are generally relatively simple toconstruct. Furthermore, displacing the magnet poles in a rotationallysymmetrical manner allows other design considerations, such as thepredictability of behavior and the minimization of harmonic generation,to be satisfied while also allowing a significant reduction in the levelof cogging to be achieved. The importance of these other designconsiderations means the rotationally symmetrical displacement of themagnet poles is often preferred when mechanical balance is not animportant issue in the design of an electrical machine according to thisinvention, for example in large low-speed machines

The displacement of the magnet poles in an electrical machine affectsnot only the cogging torque but also a number of other designconsiderations. Therefore, the selection of a displacement pattern ofthe magnet poles for any electrical machine according to this inventionwill generally require a compromise between the reduction in the coggingtorque and these other design considerations. Examples of suchconsiderations are the harmonic content of the e.m.f. waveform createdin the stator winding if the machine is a generator, the harmoniccontent of the m.m.f. created by the stator winding if the machine is amotor and the cost and complexity of the construction of the machine.

As an example of such design considerations, the following discussionrefers to the issues affecting the e.m.f. waveform created in thewinding of a generator.

When the magnet poles and the winding slots of a generator are uniformlyspaced, as in a conventional generator, the circumferential m.m.f. forcepattern created by the rotor during the operation of the generatorcontains only the fundamental magnet pole number frequency and its oddharmonics. However, if the winding slots are uniformly spaced and themagnet poles are not, as is possible in machines according to thisinvention, then other frequencies will also be present. This can causean excessive distortion of the voltage waveform in the stator windingarising from sub-harmonic frequencies and multiples thereof. However, asdiscussed below, it is possible that the stator winding phases inelectrical machines according to this invention may be connected suchthat a substantial portion of the unwanted frequencies are eliminated orminimized

The stator winding phases in an electrical machine may be connected inone, or more, parallel circuits in which the coils are connected so asto minimize the harmonic content of the e.m.f. waveform generated in thestator winding. For example, if the selected displacement pattern of themagnet poles of a generator according to this invention is such thatthere is a plurality of groups of magnet poles that each contain thesame number of magnet poles and each have the same displacement pattern,then it is preferred that the stator winding phases are connected suchthat the number of winding pole groups in series in each circuit isequal to, or is a multiple of, the number of magnet poles in each groupof magnet poles. This connection of the stator winding phases ensuresthat the e.m.f. waveform created in the stator winding contains only thefundamental pole number frequency and its integral harmonics.

Furthermore, as the displaced magnet poles may lead to even harmonics intheir m.m.f. pattern, the use of 100% pitched stator coils, that is,coils that have their two sides in winding slots which are separated bythe reference angular pitch of the magnet poles, may be preferred asthey ensure that the e.m.f. waveform created in the stator winding doesnot contain even harmonics of the fundamental pole number frequency.

The use of a star-connected 3-phase stator winding would ensure that the3^(rd) harmonic of the fundamental pole number frequency and itsintegral multiples (triple-n harmonics) could not flow in the statorcurrent and that a generator with a stator winding connected in this waywould not have triple-n harmonics in its line-line voltage waveform.This specific winding is given as an example only. The effect on thee.m.f. harmonics of different winding configurations and windings withdifferent numbers of phases is well known and would be readilyunderstood by those who are skilled in the art.

Alternatively, pitching the stator coils at two-thirds of the referenceangular pitch of the magnet poles would also eliminate the generation oftriple-n harmonics in the stator e.m.f. as would certain forms ofinterleaved (or interspersed) windings, details of which are availablein “Alternating Current Machines” by M. G. Say and would be well knownto a person skilled in the art. However, having stator coils pitched attwo-thirds of the reference angular pitch of the magnet poles in thisway leads to a significant reduction in the rated power of the machineand the forms of interleaved windings that eliminate the triple-nharmonics are usually impractical for application in large scalemachines with a high number of magnet poles.

In this way, a generator according to this invention that has adisplacement pattern of the magnet poles such that there is a pluralityof groups of magnet poles each group containing the same number ofmagnet poles and the same displacement pattern and that has 100% pitchedstator coils, a star connected 3-phase stator winding and stator coilsthat are connected such that the number of winding pole groups in seriesin each circuit is equal to, or is a multiple of, the number of magnetpoles in each group of magnet poles, would create an e.m.f. waveform inthe stator winding that contains only the fundamental pole numberfrequency, and its 5^(th), 7^(th), 11^(th), 13^(th) etc. harmonics whenoperated.

It is to be understood that the above discussion of the number andconnection of the stator winding phases and the pitching of the statorcoils to control the harmonics in the e.m.f. waveform created in thestator windings is not intended to be exhaustive and is included only asan example of the considerations involved in the specific design of agenerator according to this invention. The methods of connecting thestator winding phases and pitching of stator coils in order to minimizeunwanted harmonics in the e.m.f. waveform created in the stator windingof a generator are well known and could readily be applied to thisinvention by a person skilled in the art. Furthermore, it is also to beunderstood that, although the above section discusses the minimizationof undesirable harmonics in the e.m.f. waveform created in the statorwinding of a generator according to this the invention, the designconsiderations for the minimization of undesirable m.m.f. harmonicscreated by the stator winding in a motor according to this invention areexactly equivalent. A person skilled in the art would immediately beable to apply the methods discussed above to a motor according to thisinvention in order to minimize the undesirable m.m.f. harmonics in ananalogous manner.

Furthermore, despite the possibility of elimination of a substantialportion of the unwanted harmonic content of the e.m.f. waveform createdin generators according to this invention and the m.m.f. created bymotors according to this invention using the above methods, it may stillbe necessary to select a magnet pole displacement pattern that resultsin a cogging torque greater than the minimum possible in order toachieve an acceptable harmonic content. At present this is possiblebecause an acceptable reduction in cogging can be achieved by therelatively simple displacement patterns of magnet poles disclosed below.These patterns do not reduce the cogging torque to the absolute minimumpossible but provide a significant reduction in the cogging torquewhilst also being acceptable with respect to other designconsiderations. However, it is to be appreciated that, in some cases, itmay be required to reduce the level of cogging further and then otherdisplacement patterns may be preferred. For example, displacementpatterns that contain larger groups of poles or have groups containingdifferent numbers of poles may be preferable and these arrangements areequally possible according to this invention.

One set of preferred embodiments of a rotor according to this inventionhas a plurality of magnet pole groups, each group including eight magnetpoles and having the same displacement pattern. This displacementpattern provides a relatively simple construction of a rotor, asignificant reduction in cogging and is preferably used in conjunctionwith a stator winding with parallel circuits of eight poles or multiplesthereof. A preferred displacement pattern for each magnet pole groupcontained in the rotor formed in this manner is as follows:

Magnet pole no. within each group 1 2 3 4 5 6 7 8 Clockwise displacementfrom 0 ¼ ½ ¾ ¾ ½ ¼ 0 reference position (reference angular winding slotpitches)

A rotor with its magnet poles displaced according to this pattern willhave one quarter of its magnet poles that are not displaced and aresituated in their reference positions. Three quarters of the magnetpoles will be displaced magnet poles and of these one quarter will bedisplaced from their reference position by ¼ of the reference angularwinding slot pitch (i.e., the reference angular pitch of the windingslots), one quarter will be displaced by ½ of the reference angularwinding slot pitch and the final quarter will be displaced by ¾ of thereference angular winding slot pitch. Therefore, this displacementpattern increases the number of preferred low potential energy positionsbetween the rotor and the stator by a factor of four as compared to amachine with magnet poles spaced uniformly around the circumference.This results in a four-fold increase in the cogging frequency. However,more importantly, this displacement pattern also results in asignificant reduction in the difference in the magnitudes of theattraction between the rotor and the stator when the rotor is in its lowand high potential energy positions relative to the stator. This leadsto a substantial and significant reduction in the magnitude of thecogging torque when a machine according to this invention with itsmagnet poles displaced according to the above pattern is operated.

Finite element analysis of this displacement pattern has shown that itis particularly effective in electrical machines that contain uniformlyspaced winding slots, three winding slots for each magnet pole, havemagnet poles that are ¾ of the width of the reference angular magnetpole pitch (i.e., the reference angular pitch of the magnet poles) andhave winding slot openings that have a circumferential width that is ½of the reference angular winding slot pitch.

This displacement pattern can be understood as each magnet pole beingdisplaced from its nominal reference position in the same direction byan amount according to the following formula:

$D = \frac{2\left( {p - 1} \right)}{N}$

where:

D=the angular displacement (in winding slot pitches) of the magnet polep from its reference position;

N=the number of magnet poles in the group; and

p=the magnet pole number within the group, counted from the closestadjacent magnet pole group.

(The values of p for a group of eight magnet poles can be understoodwith reference to FIG. 1, which shows the p value for each magnet polein a group of eight magnet poles in a machine according to thisinvention. However, it will be readily appreciated that thecircumferentially outermost magnet pole in each group is the firstmagnet pole number (i.e., p=1) and that, in this case, the angulardisplacement is zero, meaning that the circumferentially outermostmagnet pole is located at its reference position as explained above.)

This formula can be applied to any group of magnet poles that containsat least four magnet poles. It provides a displacement patternconsisting of a progressive increase in the angular displacement of thepoles around each group, followed by an equivalent progressive decreaseback to zero. A progressive increase in angular separation followed byan equivalent progressive decrease is preferred as it may ensureadequate separation of the magnet poles if combined with an appropriatechoice of magnet pole width.

The required angular separation between adjacent magnet poles depends onthe specific design of each electrical machine. Generally, the requiredseparation is primarily determined by the need to control the magnitudeof flux leakage between adjacent poles. That is, in order to keep fluxleakage between adjacent poles within acceptable design parameters, itis usually preferable that adjacent magnet poles are substantiallyseparated. However, it is to be understood that it is possible toconstruct electrical machines according to this invention which containpairs of adjacent magnet poles that are in contact with, or closeproximity to, one another.

The fixings used to attach the magnet poles to the rotor surface mayalso affect their angular spacing and, hence, the selection of thedisplacement pattern of the magnet poles.

As the minimum separation of the magnet poles according to thisinvention is determined by the above considerations, theseconsiderations also help determine the maximum displacement of anyindividual magnet pole from its reference position. Although the abovedisplacement pattern, as defined by the above formula, requires that nomagnet pole is displaced by more than the reference angular winding slotpitch, it is to be understood that displacement patterns containingmagnet poles displaced by more than this amount are possible as long asthe minimum desired angular separation of the magnet poles ismaintained. For example, in machines according to this invention byhaving a displacement pattern of magnet poles that contains groups oftwelve or more magnet poles, it is possible to have magnet polesdisplaced by more than the reference angular winding slot pitch withoutreducing the minimum spacing between any two adjacent magnet poles byless than one quarter of the reference angular winding slot pitch, asshown in the displacement pattern below.

Magnet pole no. within each group 1 2 3 4 5 6 Clockwise displacementfrom reference 0 ¼ ½ ¾ 1 5/4 position (angular winding slot pitches)Magnet pole no. within each group 7 8 9 10 11 12 Clockwise displacementfrom reference 5/4 1 ¾ ½ ¼ 0 position (angular winding slot pitches)

Alternatively, groups of magnet poles containing other than eight magnetpoles and displaced according to the formula above may be utilized inorder to satisfy the design considerations of specific embodiments ofelectrical machines according to this invention, as discussed earlier.For example, it may be necessary to have ten poles in each parallel pathin the stator winding in order to have a satisfactory coilconfiguration. In this case, the displacement pattern might be:

Magnet pole no. within each group 1 2 3 4 5 6 7 8 9 10 Clockwisedisplacement 0 ⅕ ⅖ ⅗ ⅘ ⅘ ⅗ ⅖ ⅕ 0 from reference position (angularwinding slot pitches)

However, it is to be understood that displacement patterns other thanthose defined above are possible. Specifically, other displacementpatterns in accordance with this invention that also satisfy the coilconfiguration requirements are also possible. Furthermore, it is also tobe understood that the displacement patterns described above are onlygiven as examples and are not intended to be limiting. An almostunlimited number of displacement patterns are possible and althoughthese are not explicitly considered in this specification, they may eachbe equally possible in the construction of electrical machines accordingto this invention.

The effectiveness of any displacement pattern of magnet poles will bedependent on the specific construction and operation of the specificelectrical machine in which it is incorporated. It is intended that thepreferred displacement pattern for any given machine may be found usingconventional techniques that are well known to people skilled in theart, for example finite element techniques. However, due to the designconsiderations discussed above it is currently envisaged that it will begenerally preferable that machines according to this invention havegroups of magnet poles that each contain the same number of magnet polesand have the same displacement pattern of magnet poles within the groupand that the number of winding pole groups connected in each parallelpath is either equal to, or is an integral multiple of, the number ofmagnet poles in each group.

An electrical machine according to this invention may also incorporateother features that reduce cogging. For example, the magnet poles may beskewed such that they are not parallel to the axis of the rotor or themagnet poles may be shaped to reduce cogging.

Machines according to this invention may be either generators or motorsand they may be used for a variety of purposes. One preferred embodimentof the invention is a low-speed large-diameter electric generator withone hundred and twelve magnet poles and three hundred and thirty-sixwinding slots as described below.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments of the invention will now be described, withreference to the accompanying drawings, in which:

FIG. 1 shows the value of p for each magnet pole in a group of eightmagnet poles;

FIG. 2 is a partial cross-section of a low speed large diameterelectrical generator of conventional construction;

FIG. 3 is a close-up view of a section of FIG. 2;

FIG. 4 is a partial cross-section of a low speed large diameterelectrical generator according to a first aspect of this invention thatis of substantially the same construction as the conventional generatorshown in FIGS. 1 and 2;

FIG. 5 is a schematic of a section of the generator of FIG. 4; and

FIG. 6 is a schematic of a section of a low speed large diameterelectrical generator according to a second aspect of this inventionwhere the rotor is located radially outside the stator.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A typical conventional construction of a low-speed large-diameterelectrical generator 1 is shown in FIGS. 2 and 3. The rotor 2 has onehundred and twelve magnet poles 3 mounted around its outer rim 4. Themagnet poles 3 are equally spaced from each other such that they areequally spaced around the circumference of the rim 4. That is, themagnet poles 3 are each positioned in their reference positions and thereference angular magnet pole pitch is 3.21° (360°/112). The rotor 2 isrotatably mounted within a stator 5 and there is an air gap 7 formedbetween the inner surface of the stator 5 and the outer surface 8 of themagnet poles 3. The stator 5 contains three hundred and thirty-sixequally spaced winding slots 6 formed in its inner surface, i.e., threewinding slots per magnet pole. This equates to a reference angularwinding slot pitch Sp of 1.07°, a third of the magnet pole pitch. Eachwinding slot 6 contains a portion of a stator winding (not shown) andthe winding slots are also equally spaced around the circumference ofthe inner surface of the stator 5. As can be seen in FIG. 3, the windingslots 6 are approximately half the width of the winding slot pitch Spand the magnet poles 3 are approximately four fifths of the width of themagnet pole pitch.

As can be seen in FIGS. 4 and 5, a low-speed large-diameter electricalgenerator according to this invention is of substantially identicalconstruction to the conventional generator shown in FIGS. 2 and 3,except that the magnet poles have an angular width that is approximatelyequal to 2.25 winding slot pitches and some of the magnet poles 3 aredisplaced and are not in their reference positions. Specifically, theone hundred and twelve magnet poles 3 are positioned in fourteenidentical groups of eight magnet poles, and each magnet pole 3 withineach group is angularly displaced in the clockwise direction from itsreference position by an amount according to the formula:

$D = \frac{2\left( {p - 1} \right)}{N}$

where:

D=the angular displacement (in winding slot pitches) of the magnet polep from its reference position;

N=the number of magnet poles in the group; and

p=the magnet pole number within the group, counted from the closestadjacent magnet pole group.

Pole 3 a is the first pole in its group and is therefore positioned inits reference position. That is, D=0 as N=8 and p=1. Pole 3 b is thesecond pole in the group (N=8 and p=2) and pole 3 c (N=8 and p=3) is thethird; therefore, they are displaced from their reference positions byone quarter of the winding slot pitch Sp and one half of the windingslot pitch Sp, respectively.

A complete group of magnet poles 3 of an electrical machine according tothis invention are represented in FIG. 5. The two end poles 3 a, 3 h arepositioned in their reference positions while the middle six poles 3 bto 3 g are displaced to the right of their reference positions byvarying amounts. Poles 3 b and 3 g are displaced by one quarter of thewinding slot pitch Sp, poles 3 c and 3 f by one half of the winding slotpitch Sp and poles 3 d and 3 e by three quarters of the winding slotpitch Sp.

A low-speed large-diameter electrical machine having an alternativeconfiguration is shown in FIG. 6. The rotor 9 has one hundred and twelvemagnet poles 10 mounted around its inner rim 11. The rotor 9 isrotatably mounted around a stator 12 and there is an air gap 13 formedbetween the outer surface of the stator 12 and the outer surface 14 ofthe magnet poles 10. The stator 12 contains three hundred and thirty-sixequally spaced winding slots 15 formed in its outer surface. Eachwinding slot 15 contains a portion of a stator winding (not shown) andthe winding slots are equally spaced around the circumference of theinner surface of the stator 12. This equates to a reference angularwinding slot pitch Sp of 1.07°.

The magnet poles 10 have an angular width that is approximately equal to2.25 winding slot pitches and some of the magnet poles 10 are displacedand are not in their reference positions. Specifically, the one hundredand twelve magnet poles 10 are positioned in fourteen identical groupsof eight magnet poles and each magnet pole 10 within each group isangularly displaced in the clockwise direction from its referenceposition by an amount according to the formula:

$D = \frac{2\left( {p - 1} \right)}{N}$

where:

D=the angular displacement (in winding slot pitches) of the magnet polep from its reference position;

N=the number of magnet poles in the group; and

p=the magnet pole number within the group, counted from the closestadjacent magnet pole group.

Pole 10 a is the first pole in its group and is therefore positioned inits reference position. That is, D=0 as N=8 and p=1. Pole 10 b is thesecond pole in its group and is displaced to the right of its referenceposition by one quarter of the winding slot pitch Sp. Pole 10 c is thethird pole in its group and is displaced to the right of its referenceposition by one half of the winding slot pitch Sp. Pole 10 d is thefourth pole in its group and is displaced to the right of its referenceposition by three quarters of the winding slot pitch Sp. Thedisplacement for poles 10 a-10 d is determined with reference to theadjacent magnet pole group that is to the left of the group underconsideration. However, for poles 10 e-10 h, the displacement isdetermined with reference to the adjacent magnet pole group that is tothe right of the group under consideration. Pole 10 e is the fourth polein its group when counted from the closest adjacent magnet pole groupand is displaced to the right of its reference position by threequarters of the winding slot pitch Sp. Pole 10 f is the third pole inits group and is displaced to the right of its reference position by onehalf of the winding slot pitch Sp. Pole 10 g is the second pole in itsgroup and is displaced to the right of its reference position by onequarter of the winding slot pitch Sp. Pole 10 h is the first pole in itsgroup and is positioned in its reference position.

The displacement pattern of each group of magnet poles may therefore berepresented as follows:

Magnet pole no. within each group 1 2 3 4 5 6 7 8 Magnet pole reference10a 10b 10c 10d 10e 10f 10g 10h Clockwise displacement from reference 0¼ ½ ¾ ¾ ½ ¼ 0 position (reference angular winding slot pitches)

It will be appreciated that none of the magnet poles are displaced fromtheir reference position by an integral multiple of the winding slotpitch Sp.

For improved clarity, each of the poles 10 a-10 h is shown ghosted as itwould appear if located at is respective reference position so that thedisplacement of each pole from that reference position can be easilyidentified.

1. An electrical machine including a first body having a plurality of circumferentially spaced magnet poles formed at its radially inner surface, and a second body, that is located within the first body, and having a plurality of circumferentially spaced winding slots formed at its radially outer surface, one of the first body and the second body being a rotor and rotatably mounted, and the other of the first body and the second body being a stator and being fixedly mounted, the winding slots having a reference angular pitch that is equal to 360° divided by the number of winding slots in the electrical machine; the magnet poles comprising at least a first group including at least two circumferentially adjacent magnet poles and a second group including at least two circumferentially adjacent magnet poles; each magnet pole having a reference position wherein the reference positions are equally spaced around the circumference of the first body; at least one magnet pole in each of the first and second groups being a circumferentially outermost magnet pole and being located in its reference position; and at least one magnet pole in each of the first and second groups being a displaced magnet pole and being located in a position that is displaced from its reference position by an amount that is not equal to an integral multiple of the reference angular pitch of the winding slots.
 2. The electrical machine according to claim 1, wherein the stator has the winding slots and the rotor has the magnet poles.
 3. The electrical machine according to claim 1, wherein the first body is the stator and the second body is the rotor.
 4. The electrical machine according to claim 1, wherein the first body is the rotor and the second body is the stator.
 5. The electrical machine according to claim 1, wherein no magnet pole is displaced from its reference position by more than the reference angular pitch of the winding slots.
 6. The electrical machine according to claim 1, wherein no two adjacent magnet poles are in contact with, or impinge upon, each other.
 7. The electrical machine according to claim 1, wherein a displacement pattern of the magnet poles around a circumference of the first body has at least two-fold rotational symmetry about a rotational axis of the rotor.
 8. The electrical machine according to claim 1, wherein the first group includes at least four magnet poles and the second group includes at least four magnet poles.
 9. The electrical machine according to claim 8, wherein both circumferentially outermost magnet poles in each of the first and second groups are located in their reference positions.
 10. The electrical machine according to claim 1, wherein the first group includes an even number of magnet poles and the second group includes an even number of magnet poles.
 11. The electrical machine according to claim 1, wherein the first group and the second group include the same number of magnet poles.
 12. The electrical machine according to claim 11, wherein winding phases of the machine are connected in a plurality of parallel circuits such that the number of winding pole groups in series in each circuit is equal to, or is an integral multiple of, the number of magnet poles in each group of magnet poles.
 13. The electrical machine according to claim 11, wherein the first group includes eight magnet poles and the second group includes eight magnet poles.
 14. The electrical machine according to claim 11, wherein a displacement pattern of the magnet poles in the first group is the same as a displacement pattern of the magnet poles in the second group.
 15. The electrical machine according to 14, wherein the displacement pattern of the magnet poles in the first and second groups is determined according to the formula: $D = \frac{2\left( {p - 1} \right)}{N}$ where: D=the angular displacement (in winding slot pitches) of magnet pole p from its reference position; p=the magnet pole number within the first or second group, counted from the closest adjacent magnet pole group; and N=the number of magnet poles in the first or second group.
 16. The electrical machine according to claim 1, wherein the winding slots are uniformly circumferentially spaced.
 17. The electrical machine according to claim 1, wherein the magnet poles have a reference angular pitch that is equal to 360° divided by the number of magnet poles in the electrical machine, and further comprising winding coils that have an angular pitch equal to the reference angular pitch of the magnet poles.
 18. The electrical machine according to claim 1, wherein the magnet poles have a reference angular pitch that is equal to 360° divided by the number of magnet poles in the electrical machine, and further comprising winding coils that have an angular pitch equal to two-thirds of the reference angular pitch of the magnet poles.
 19. The electrical machine according to claim 12, wherein the number of winding slots is equal to an integral multiple of the product of the number of magnet poles and the number of winding phases.
 20. The electrical machine according to claim 19, wherein there are three times as many winding slots as magnet poles.
 21. The electrical machine according to claim 1, wherein each magnet pole is formed by permanent magnets, and wherein an angular width of each permanent magnet is substantially 2¼ times the reference angular pitch of the winding slots.
 22. The electrical machine according to claim 1, further comprising an air gap between the first body and the second body, and wherein a width of each winding slot at the air gap is substantially equal to one half of the reference winding slot pitch.
 23. The electrical machine according to claim 1, wherein each magnet pole is substantially parallel to the rotational axis of the rotor.
 24. The electrical machine according to claim 1, wherein each magnet pole is skewed relative to the rotational axis of the rotor.
 25. The electrical machine according to claim 1, wherein magnetic slot wedges are incorporated in the winding slots.
 26. The electrical machine according to claim 1, further comprising an air gap between the first body and the second body, and wherein the outer surface of each magnet pole is shaped such that the air gap is not uniform. 